Question

Michael is running for president. The proportion of voters who favor Michael is 0.8. A random sample of 100 voters is taken.

Answer 1

Answer:

Michael is running for president. The proportion of voters who favor him is 0.3. A simple random sample of 100 voters is taken.

a)

What is the expected value :: n*p = 100*0.8 = 80

standard deviation:: sqrt(n*p*q) = sqrt(80*0.2) = 16

where q is proportion of voters who do not favor Michael. (q=0.2)

and shape of the sampling distribution is binomial distribution  which is  approximately a  bell shaped.

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what is the probability that the number of voters in the sample who will not favor Michael will be more than 16

P(X < 16.0) = P((x - 20) / 4.0) < (16.0 - 20) / 4.0) = P(Z < -1.00) = .1587        

P(X > 16.0) = 1 - 0.1587 = 0.8413